Will LNK2 plug into an original ESP-TM?

No. Buy ESP-TM2, then LNK2. The old ESP-TM door has no LNK Ready port.

TM2 or RC2 for an 8-zone ESP-TM swap?

RC2 if they want Wi-Fi in one SKU and will stay at eight valves. TM2-8 if they want a familiar panel and may add LNK2 later. ME3 if they might grow or want flow.

Does TM2 take FG100 flow?

No. FG100 is the ME3 (and compatible commercial) pair on this shop.

Replace an ESP-TM with ESP-TM2 + LNK2

There is no LNK2 retrofit for the original ESP-TM. Hang an ESP-TM2 in the same 4-, 6-, 8-, or 12-station count, then add LNK2WIFI when they want the app. WaterSense on this path is TM2 + LNK2 + a Rain Bird rain sensor (WR2-48 is the usual pair). Station count is still fixed — move to ESP-ME3 if the site will grow or needs FG100 flow.